Just received a couple of stainless steel G.A.K. stoves which are intended for use with round/cylindrical water bottles.

Search "G.A.K. New Stainless Steel Bottle Backpacking Stove" on amazon.

It appears the stove will "nest" directly with many common water bottles, and perhaps "nest" over some cups which are slipped onto the base of the water bottle.

Strongly suggest reading the reviews for further info/applications; quite informative, IMHO.

Well-made of stout stainless steel, with appropriate venting holes near the top.

Other stoves can certainly do, but this item has the additional feature of being a "windblocker" which is always useful when using alcohol burners.  It is certainly possible to use this stove with heat tabs.  Using it as a "twig-burner" might be possible, although likely requiring much "tending".  Still, multi-fuel capability is a plus, IMHO.

OEM shiny SS finish can be subdued with sandpaper or bead blasting, as you please.

FWIW, I often paint the exterior of many Stainless Steel metal cooking items with black HI-Temp "Exhaust Header" paint, after prepping the metal surface.  The Black paint allows somewhat faster heating of the contents, reduced use of fuel, and also allows somewhat easier removal of grime.

Disclaimer: No financial interest.

ETA: Some possible tweaks for the GAK stove: Tweaks

ETA2:  This stove will fit the bottom of the wide-mouthed 38 Oz Stainless steel Nalgene bottle.  It may fit over some cups which are "nested" on the bottom of the bottle, but user may need to widen/deepen the cut-out in the stove to accommodate the bracket for the cup's handles.  In lieu of a cup, the user might choose to select a smallish pot with both handles and bail which will fit over both bottle and bottom-nested stove.

OTOH, and if all else fails, the stove will fit over the neck of the abovementioned bottle IF the user removes the OEM cap and its' tether and installs a much more useful plastic "humangear CapCAP" (amazon).  This accessory allows a smaller, slosh-resistant drinking port, as well as access to the wide mouth.  It does add some height, but little, if any weight.  The stove, being slipped over the mouth of the bottle does not prevent the humangear CapCap from sealing properly.  The device is highly recommended but be sure to make sure to order the correct cap for your application.  

I find it interesting and enjoyable to tinker with these devices.  I hope the results prove useful.

G.A.K New Stainless Steel Bottle Backpacking Stove

amazon link for others^

neat idea. I added it to my list, thx OP. Random thoughts but it reminds me of my days making pop can alcohol stoves / cat stoves etc.

also saw how cheap knock off trangia type alcohol stoves are now.

anybody have on of those stamped / flat fold puzzle together type stoves?

I should go add one of those to my list too. :)

Best reviews of Trangia-type stoves I've seen are by Hiram Cook (dated but invaluable as a foundation) and PaleoHikerMD (modern reviews) both on YouTube.

Best fold-flat type stoves are probably made by Firebox company.  See PaleoHikerMD channel for reviews of their products.

Significant content added to OP above in ETA2.